a quarterback throws a football to a teammate. the football is 6.5ft above the ground when it leaves the…

a quarterback throws a football to a teammate. the football is 6.5ft above the ground when it leaves the quarterbacks hand. his teammate catches it 3.5s later, at a height above the ground of 5 ft. projectile motion formula (h(t)=-16t^{2}+vt + h_{0}) (h_{0}=6.5) (v =?) (h = 5) when (t = 3.5) determine the value of (v), rounded to the nearest whole number.

a quarterback throws a football to a teammate. the football is 6.5ft above the ground when it leaves the quarterbacks hand. his teammate catches it 3.5s later, at a height above the ground of 5 ft. projectile motion formula (h(t)=-16t^{2}+vt + h_{0}) (h_{0}=6.5) (v =?) (h = 5) when (t = 3.5) determine the value of (v), rounded to the nearest whole number.

Answer

Explanation:

Step1: Substitute given values into formula

Substitute $h = 5$, $t = 3.5$, and $h_0=6.5$ into $h(t)=-16t^{2}+vt + h_0$. We get $5=-16\times(3.5)^{2}+v\times3.5 + 6.5$.

Step2: Simplify the equation

First, calculate $-16\times(3.5)^{2}=-16\times12.25=-196$. The equation becomes $5=-196 + 3.5v+6.5$.

Step3: Combine like - terms

Combine the constant terms on the right - hand side: $5=-189.5 + 3.5v$.

Step4: Isolate the term with $v$

Add $189.5$ to both sides of the equation: $5 + 189.5=3.5v$, so $194.5 = 3.5v$.

Step5: Solve for $v$

Divide both sides by $3.5$: $v=\frac{194.5}{3.5}\approx55.57$.

Step6: Round to the nearest whole number

Rounding $55.57$ to the nearest whole number gives $v\approx56$.

Answer:

$56$